4.1 Data

The GVAR framework captures the spillover and feedback effects between uncertainty and unemployment within and across states. The model is estimated using two variables for each state: state-level uncertainty and the state-level unemployment for 51 US states from 2006M01 to 2018M03. Uncertainty for each state is measured according to the method outlined in Section 2 and is in a levels form. Unemployment is measured as the 3-month change in the unemployment rate, measured every month to ensure the stability of the GVAR responses.Footnote ¹² The flexibility of this GVAR framework is that it also allows for a relatively parsimonious reduced form representation of the macroeconomy through the accommodation of the effects of aggregate variables—such as interest rates or inflation, for instance, without their necessary explicit inclusion. In essence, to the extent that such aggregate variables are important determinants of state-specific unemployment, their heterogenous effects will be captured through current and lagged values of the starred variables.Footnote ¹³

Due to the short time span of the Google search data, the maximum $p_{i}$ is 2 and the maximum $q_{i}$ is 1 following Dees et al. (Reference Dees, Mauro, Pesaran and Smith2007).Footnote ¹⁴ Based on the Akaike information criterion (AIC), a VARX^*(1,1) is fitted to most states. A specification search is also performed on the coefficients and insignificant coefficients for which the absolute value of the $t$ -ratio being less than 1 are excluded from the model.Footnote ¹⁵

4.2 Assessing the Adequacy of the Disaggregate Model

4.2.1 Joint significance

The joint significance of the foreign variables

GVAR models allow for potentially important cross-state interaction information that cannot be explicitly captured in more aggregate models. As described earlier, the presence of the starred or foreign variables allow uncertainty and unemployment to be interconnected across states that are represented by the coefficient matrices $\Lambda$ . To investigate the statistical importance of these variables, however, the joint significance of cross-state interactions is calculated through an F-test of the joint significance of starred uncertainty variables and starred unemployment variables in each of the uncertainty and the unemployment equations for each of the individual state models.

Table 2 reports the F-test statistics associated with testing of the following null: $H_{0}:\Lambda _{i0}^{\tau }=\Lambda _{i1}^{\tau }=0$ for $i=1,\ldots,N$ and for $\tau =1,\ldots,4$ .Footnote ¹⁶ The table shows that there is significant statistical evidence showing the importance of starred uncertainty and starred unemployment in each of the state-specific equations. In other words, there is evidence of substantial interaction of economic activity and behavior across disaggregate units and therefore gives support to the use of the GVAR modeling approach as an appropriate framework to capture these complex interactions.

Table 2. F-test statistics on the joint significance of national uncertainty ( $us^*$ ) and national unemployment ( $ur^*$ )

Notes: This shows the F-test statistics of the joint significance of national uncertainty ( $us*$ ) and national unemployment ( $ur*$ ) of the state-level uncertainty and unemployment equations $^{***}p\lt 0.01$ , $^{**}p\lt 0.05$ , $^{*}p\lt 0.1$ .

The Joint Significance of the State-Specific Uncertainty Variables

Given there are substantial interactions between uncertainty measures across states, we next investigate whether our state-specific uncertainty measures provide meaningful information content in describing the variation in uncertainty above and beyond the information already provided by the aggregate or common factor element. To investigate the statistical importance of the idiosyncratic uncertainty component, therefore, the joint significance is calculated through an F-test of the joint significance of state-specific uncertainty in each of the uncertainty and the unemployment equations for each of the individual state models.

Table 3 reports the F-test statistics associated with testing of the following null: $H_{0}:\Phi _{i1}^{\upsilon }=\Phi _{i2}^{\upsilon }=0$ for $i=1,\ldots,N$ and for $\upsilon =1,2$ .Footnote ¹⁷ The table shows that there is significant statistical evidence showing the importance of idiosyncratic uncertainty component in almost all states. On the whole, despite the substantial interaction of economic activity across states, there is evidence that the idiosyncratic components also provide meaningful contributions in explaining fluctuations in state-level economic activity and uncertainty.

Table 3. F-test statistics on the joint significance of state-specific uncertainty ( $us$ )

Notes: This shows the F-test statistics of the joint significance of state uncertainty ( $us$ ) of the state-level uncertainty and unemployment equations $^{***}p\lt 0.01$ , $^{**}p\lt 0.05$ , $^{*}p\lt 0.1$ .

4.2.2 Predictive criteria

This section makes use of a statistical criterion to investigate the usefulness of disaggregate data in understanding the effect of uncertainty at the US state and national level. While a well-specified disaggregated model will generally outperform an aggregate model, if the disaggregate model is misspecified, this may not hold. For instance, a disaggregate model may be misspecified if macroeconomic influences are incorrectly omitted or if measurement errors found in the disaggregate model cancel out in the aggregate. The inclusion of the global variables in the GVAR model means that the first will unlikely to be a problem; however, the second might be potentially relevant due to the sample size of the Google data. The prediction criteria test proposed in PPK assesses the ability of a disaggregate model in predicting an aggregate series of interest, relative to the ability of an aggregate model, under the null that the disaggregate model is true.

In this context, assume that each state, $i,$ is modeled according to the VARX* model specified earlier and that the aggregate model is assumed to be estimated of the following vector form:

(4) \begin{equation} y_{t}=c_{t}+\mathbf{a}y_{t-1}+\mathbf{b}y_{t-2}+\mathbf{e}_{t}. \end{equation}

where $y_{t}=\left (US_{t},UR_{t}\right )$ , $US_{t}=\sum _{i=1}^{s}w_{i}us_{i,t}$ and $UR_{t}=\sum _{i=1}^{s}w_{i}ur_{i,t}$ .Footnote ¹⁸

In PPK, the following statistics are used to rank the disaggregate model and the aggregate model:

(5) \begin{equation} s_{a}^{2}=\frac{\mathbf{e_{t}}^{\prime }\mathbf{e_{t}}}{T-\kappa _{a}}, \end{equation}

(6) \begin{equation} s_{d}^{2}=\sum _{i,j=1}^{N}\frac{\sum \limits _{t=1}^{n}(w_{i}u_{it})^{\prime }w_{j}u_{jt}}{T-\kappa _{i}-\kappa _{j}+tr(A_{i}A_{j})} \end{equation}

where $T$ is the number of observations, $\kappa _{a}$ is the number of estimated parameters in the aggregate model, $\kappa _{i}$ is the number of unrestricted parameters in each disaggregate model, and $A_{i}=X_{i}(X_{i}^{\prime }X_{i})^{-1}X_{i}^{\prime }$ , and $X_{i}$ is the matrix which consists of the explanatory variables in the $i$ -th equation. These statistics have the property that on average $s_{a}^{2}\gt s_{d}^{2}$ if the disaggregate model is true. Lee and Shields (Reference Lee and Shields1998) transform $s_{a}^{2}$ and $s_{d}^{2}$ to statistics that are comparable to $R^{2}$ measures:

(7) \begin{equation} r_{a}^{2} =1-\frac{s_{a}^{\text{2}}}{\sum \limits _{t=1}^{T}\left [ y_{t}-\overline{y_{t}}\right ] ^{2}/\left [ T-\kappa _{a}\right ]},\text{ and} \end{equation}

(8) \begin{equation} r_{d}^{2} =1-\frac{s_{d}^{\text{2}}}{\sum \limits _{t=1}^{T}\left [ y_{t}-\overline{y_{t}}\right ] ^{2}/\left [ T-\kappa _{a}\right ]} \end{equation}

where $\overline{y_{t}}$ represents the mean of the aggregate uncertainty and unemployment series, and $r_{a}$ and $r_{d}$ denote the transformed prediction criteria for the aggregate and disaggregate model, respectively. In this case, on average, $r_{a}^{2}$ will be smaller than $r_{d}^{2}$ if the disaggregate model is true. Asymptotically, if the disaggregate model is true, the criterion discussed above will rank the models correctly, on average, but this may not hold in a finite sample. To assess this, following GLP, a simulation experiment can be carried out by simulating the distribution of the test statistic, $D_{ad}=r_{d}^{2}-r_{a}^{2},$ defining the difference between the choice criteria. Accordingly, if the disaggregate model is correctly specified, $D_{ad}\gt 0.$ However, although this will hold asymptotically, this statistic may be smaller than 0 in any particular sample simply because of sample variation.Footnote ¹⁹ Given this, GLP suggest calculating a value $d_{ad}^{\ast }(\alpha )$ obtained from the distribution of $D_{ad}$ such that the probability of selecting the disaggregate model when it is true is $(1-\alpha )$ . We do so by first simulating the data 5000 times, assuming that the structure of the disaggregate model is the true data-generating process, and sampling with replacement. At each run, the test statistic is recalculated to obtain the distribution for $D_{ad}$ , and the value of $d_{ad}^{\ast }(\alpha )$ is determined from the left tail of this distribution.

We find significant statistical evidence that the disaggregate model outperforms the aggregate model in terms of its ability to predict aggregate uncertainty and aggregate unemployment as shown in Figure 3. Figure 3 reports the predictive difference between the aggregate model and the disaggregate model in predicting uncertainty (top panel) and unemployment (middle panel)—that is $D_{ad}=r_{d}^{2}-r_{a}^{2}$ along $d_{ad}^{\ast }(\alpha )$ from the simulated distribution ( $\alpha =0.05$ ). The figure clearly shows that the disaggregate model displays a higher ability to predict uncertainty and unemployment compared to the aggregate model, as seen by positive $D_{ad}$ values (in red). Further, once random variation is taken into account, there is still significant evidence to support the use of the disaggregate model, as illustrated by the fact the test statistics for predicting uncertainty and unemployment are both larger and on the right of the left tails of the distribution, $d_{ad}^{\ast }(\alpha )$ .

Figure 3. Prediction criteria. Notes: This figure plots the observed $D_{ad}$ , which is the difference in the prediction criteria test statistic (red line) and $d^*_{ad}(\alpha )$ , which is the left tail of the simulated distribution of the prediction criteria test statistic (dotted blue line) and assesses the ability of the disaggregate model versus the aggregate model in predicting aggregate uncertainty and aggregate unemployment, respectively. The figure also plots the observed $D_{dpard}$ , which is the difference in the prediction criteria test statistic (red line) and $d^*_{dpard}(\alpha )$ , which is the left tail of the simulated distribution of the prediction criteria test statistic (dotted blue line) and assesses the ability of the disaggregate model versus the partial disaggregate model without state-level uncertainty in predicting unemployment.

In the second exercise, we specifically investigate the value-added of our state-level measures of uncertainty in the disaggregate model, which again tests for the importance of the explanatory power of state-level measures of uncertainty above and beyond that of the common component. The previous exercise showed that a disaggregate model with state-level uncertainty measures and the state-level unemployment outperforms the aggregate model in terms of predicting aggregate variables. We further investigate whether the same disaggregate model outperforms a partial disaggregate model, which does not feature state-level measures of uncertainty, in terms of predicting the aggregate unemployment variable, under the null that the full disaggregate model is true. We find significant statistical evidence that the full disaggregate model outperforms the partial disaggregate model as shown in the bottom panel of Figure 3. This is reflected in the figure by a positive $D_{dpard}$ value (in red). Further, once random variation is taken into account, there is still significant evidence to support the use of the disaggregate model, as illustrated by the fact the test statistics for predicting unemployment are both larger and on the right of the left tail of the distribution, $d_{dpard}^{\ast }(\alpha )$ .

4.2.3 Forecast performance

Table 4 presents the out-of-sample forecast performance in terms of both point forecasts, as measured by the Root Mean Squared Errors (RMSEs) and density forecasts, as measured by the Average Log Scores (ALSs) of various models in predicting aggregate unemployment at the 1-month, 3-month, 6-month, and 1-year forecast horizons in purely statistical terms. We perform the out-of-sample evaluation using a rolling window estimation scheme over two sample horizons. In the first exercise, we use half the sample period (from 2006M01 to 2012M01) as the initial sample size and forecast using a rolling window until 2015M02 (which represents 3/4 of the total sample size). In the second, observations up to 2015M02 are used as the initial period to form out-of-sample forecasts for the remaining sample. The GVAR model in equation (3) is used as the benchmark to illustrate the usefulness of our disaggregate framework as well as of our state-level GTU measures. A value less than 1 represents a superior forecasting performance. The table reports the improvement or deterioration in forecast performance of the GVAR model relative to other forecasting models, namely (i) disaggregate model of state-level unemployment using only unemployment variables (DISU); (ii) a partially disaggregated model using state-level measures of unemployment alongside the aggregate GTU measure of uncertainty (GTU); (iii)–(vi) as the model in (ii) but respectively using the EPU [Baker et al. (Reference Baker, Bloom and Davis2016)], the VIX, a measure of macroeconomic uncertainty (JLN) [Jurado et al. (Reference Jurado, Ludvigson and Ng2015a)] and a measure of financial uncertainty (LMN) [Ludvigson et al. (Reference Ludvigson, Ma and Ng2020)], in place of the GTU as the aggregate measures of uncertainty. The statistical significance of the improvement is tested using the Giacomini and White (Reference Giacomini and White2006) test of equal forecast performance.

Table 4. Evaluation of out-of-sample point and density forecasts

Notes: The upper (lower) panel reports the out-of-sample RMSE (Average Log Scores—ALS) ratio of the GVAR model relative to the RMSE (ALS) of other models. A ratio $\lt$ 1 indicates that the GVAR model outperforms other models. A " $^*$ " denotes that the RMSE (ALS) ratio for the GVAR model statistically outperforms the other models at the 10% level of significance through applying the Giacomini and White (Reference Giacomini and White2006) test of equal forecast performance. We perform the out-of-sample evaluation using a rolling window estimation scheme. $T$ is the total sample size and is out of 1 (100%) and $t0$ is the training sample size.

The top half of Table 4 presents the forecasting performance using the RMSE criterion and shows that there is not much evidence from the point forecasts. The GVAR outperforms the diasaggrate model using unemployment only (DISU) and the partially disaggregated models in the case of the measure of macroeconomic uncertainty (JLN). Only in the latter case, however, the performance is statistically significant. The bottom half of the table presents the forecasting results using the density-based ALS. The results show that the extra complexity of GVAR stemming from our state-level uncertainty measures has an important impact on forecast performance. The GVAR benchmark outperforms in five of the six models, and the forecast performance is statistically significant. There is therefore strong evidence to support the usefulness of the disaggregate model in a broad sense and, in particular, the usefulness of our measures of state-level uncertainty over and beyond the information provided by other uncertainty measures that are only available at the aggregate level.

4.3 Dynamic Impulse Response Analysis

The identification of exogenous variations of the uncertainty shock is achieved via the widely adopted time-ordering assumption. A recent paper by Carriero et al. (Reference Carriero, Clark and Marcellino2018a) shows that macroeconomic uncertainty can be considered as exogenous when assessing its effects on the US economy. Nonetheless, our general conclusions are robust to this time-ordering assumption (see Section 8 of the Appendix for further details). In addition, it is noticed that the construction of our uncertainty index includes terms such as "unemployment benefit" or "unemployment extension" which may raise endogeneity concerns. We find that it is not the case since the average correlation between the original uncertainty and the index without these unemployment-related keywords gives the value close to 0.99. In addition, following Garín et al. (Reference Garín, Lester and Sims2019), we also find that the GTU index is uncorrelated with other shocks such as total factor productivity, oil price, fiscal, or monetary policy shocks. The ordering implies that uncertainty does not respond to the unemployment shock in the impact period while allowing unemployment to respond to the uncertainty shock (while still allowing uncertainty shocks between states to be correlated). This also assigns the maximum possible effect to the uncertainty shocks and provides an upper bound on the measure of the effect of uncertainty.

Consider the GVAR(2) model in equation (3), the moving average representation is given by:

(9) \begin{equation} x_{t}=\epsilon _{t}+A_{1}\epsilon _{t-1}+A_{2}\epsilon _{t-2}+\ldots \end{equation}

and $A_{s}$ can be defined recursively as:

(10) \begin{equation} A_{s}=F_{1}A_{s-1}+F_{2}A_{s-2},\ \ s=1,2,\ldots \end{equation}

with $A_{0}$ $=I$ , $A_{s}=0$ for $s\lt 0$ .

The time-ordering assumption of the shocks allows us to separate the effects of the uncertainty shocks, denoted as $\delta _{t}=(\epsilon _{1t},\epsilon _{3t},\ldots,\epsilon _{101t})$ , from the total shocks to the GVAR by regressing $\epsilon _{t}$ on $\delta _{t}$ and writing $\epsilon _{t}=\bar{D}\delta _{t}+\tilde{\epsilon _{t}}$ . In this case, equation (9) can be rewritten in terms of "orthogonal" uncertainty shocks and other unemployment-related shocks:

(11) \begin{equation} x_{t}=\left [ \bar{D}\delta _{t}+\tilde{\epsilon _{t}}\right ] +A_{1}[\bar{D}\delta _{t-1}+\tilde{\epsilon }_{t-1}]+A_{2}[\bar{D}\delta _{t-2}+\tilde{\epsilon }_{t-2}]+\ldots \end{equation}

The impulse response function for the GVAR model can then be written as:

(12) \begin{equation} \text{IRF}(x_{t};\;u_{it},h)=\frac{e_{i}^{\prime }A{_{h}}\bar{D}\Sigma _{\delta }\bar{D}^{\prime }e_{j}}{\sqrt{e_{j}^{\prime }\Sigma _{u}e_{j}}},h=0,1,2,\ldots ;\; i,j=1,2,\ldots,2N \end{equation}

where $\Sigma _{\delta }$ denotes the variance–covariance matrix of the uncertainty shocks, $\delta _{t},$ $e_{i}$ , and $e_{j}$ are $2N\times 1$ selection vectors with unity in their $i$ -th $,$ $j$ -th elements, respectively, and zeros elsewhere, and $h$ is the horizon of the impulse. For an aggregate shock, $e_{i}$ is a vector of aggregate weights in the elements of $j=2,4,6,\ldots,2N,$ in the case of a national unemployment shock for instance, where the weights sum to 1 and where population weights are chosen to be consistent with the construction of the starred variables in the GVAR model. Given the identification assumption, the effect of a one-standard-deviation population-weighted aggregate uncertainty shock on the (weighted aggregate) unemployment variable in the GVAR model can be seen in Figure 4. For illustrative purposes, this figure also reports the traditional orthogonalized impulse response function for the bivariate VAR aggregate model showing the impact of an orthogonal uncertainty shock (defined through a Cholesky decomposition) on the unemployment variable.

Figure 4. Aggregate uncertainty shocks on aggregate unemployment. Notes: This figure compares the IRFs of a one-standard-deviation aggregate uncertainty shock in the GVAR model to the VAR model. The GVAR IRFs are the weighted response of each state unemployment to an aggregate uncertainty shock in the GVAR model, where the aggregate shock is defined in equation (12) through using population weights. The VAR IRFs are constructed via the Cholesky decomposition where uncertainty is placed first. Unemployment is defined as the quarterly change in unemployment rate. The confidence interval is the bootstrapped IRFs at $\pm 1$ s.d.

Although the effects of the respective uncertainty shocks on unemployment in both the aggregate model and the disaggregate model are similar, we find that the impact of an aggregate uncertainty shock in the disaggregate model is significantly smaller than in the aggregate model when we look at the peak response of unemployment. We find that the quarterly change in unemployment rate in the disaggregate model goes up by 0.015% point at peak, compared to 0.045% point in the aggregate model. Since unemployment is modeled as the quarterly change in the unemployment rate, we could recover the response of the actual unemployment rate to provide intuitive interpretations on the effect of uncertainty shocks. We find that the peak effect of uncertainty shock in the disaggregate GVAR model causes the unemployment rate to go up by 0.1% points. On the other hand, the unemployment rate goes up by 0.28% points in the aggregate model at peak. These findings are within the bounds of the measures documented in the literature.Footnote ²⁰

On the whole, even after assigning uncertainty to have maximum effects due to the time-ordering assumption, our results are shown to be at the more conservative end of the impact of uncertainty on economic activity. In terms of the dynamics, both impulse responses tend to start dying away after 2 years, although, the GVAR model, despite providing a smaller peak response effect, shows a far more prolonged process of dissemination of the initial shock taking approximately double the time of the impulse response from the VAR model which rapidly disseminates after approximately 2 years.

In sum, both modeling frameworks point to the significant effect of uncertainty on unemployment. The use of an aggregate model, however, shown to be misspecified in the previous section, accordingly averages over relevant feedbacks and interactions through the process of aggregation in the analysis of the impact of uncertainty on the economy and therefore overestimates the effects of uncertainty shocks relative to the disaggregate model. The aggregate model also underestimates the time it takes for the uncertainty shock to work its way through the system. As a result, the disaggregate model shows the effect of an uncertainty shock on unemployment to be statistically and significantly smaller than that according to the aggregate model and with a relatively far more prolonged dynamic response.

We close this section by observing whether there are any spatial patterns apparent in the heterogeneous responses of state-level unemployment to an aggregate uncertainty shock. In a heatmap of the USA, Figure 5 presents the median estimate of the peak response of state-level unemployment to a one-standard-deviation aggregate uncertainty shock. We find that unemployment increases in all states in response to an increase in US-wide uncertainty. The findings are also consistent to those documented in Mumtaz et al. (Reference Mumtaz, Sunder-Plassmann and Theophilopoulou2018) who find that real income declines in all states in response to an increase in US-wide uncertainty (even without accommodating for state-level uncertainty). The figure also shows that the magnitude of the increase in unemployment is largest in the coastal states. On the other hand, unemployment in more central states in the USA seems to be less affected. These heterogeneous responses in the response of unemployment to uncertainty shocks could potentially be driven by cross-state variations in financial and fiscal conditions, the industry mix, and the labor market. We investigate this in more detail in Section 5.

Figure 5. US heatmap—peak response of state-level unemployment to an aggregate uncertainty shock. Notes: This figure presents the median estimate of the peak response of state-level unemployment to a one-standard-deviation aggregate uncertainty shock.

4.4 Decomposition Analysis: State versus National Influences

In this section, we explore, for each state, the relative importance of national influences relative to state-specific influences of a national uncertainty shock on state-level economic activity. This section follows Garratt et al. (Reference Garratt, Lee and Shields2018) and characterizes the dynamic effects of specified shocks by using the variance-based persistence profile (PP) measure proposed by Lee and Pesaran (Reference Lee and Pesaran1993). The PP is used to measure the long-run response of the level series to shocks and trace out the accumulated response over time to characterize the system dynamics.

At time horizon $h$ , the PPs are defined by the $2N\times 2N$ matrix $P(h)$ and as $h\rightarrow \infty$ , converges to the following persistence matrix, in which the $(i,j)$ -th element is given by:

(13) \begin{equation} p_{ij}=\frac{e_{i}^{\prime }A(1)\Sigma _{\epsilon }A(1)^{\prime }e_{j}}{\sqrt{(e_{i}^{\prime }A(0)\Sigma _{\epsilon }A(0)^{\prime }e_{i})(e_{j}^{\prime }A(0)\Sigma _{\epsilon }A(0)^{\prime }e_{j}})}, \qquad \qquad i,j=1,\ldots,2N, \end{equation}

where $p_{ij}$ measures the infinite horizon effect of system-wide shocks to variables in the system. For instance, the permanent impact on unemployment in each state of a system-wide shock which causes the unemployment variable in each state to rise by 1 standard error on impact can be captured by considering the measures $p_{ii},$ where $i=2,4,6,\ldots 2N$ and where $i=j$ .

For the sake of brevity, the full technical details of the decomposition can be found in Section 11 of the Appendix. In this analysis, two decompositions of the persistence measure $p_{ii}$ are of interest. The first concerns the part due to orthogonalized uncertainty shocks on state unemployment dynamics relative to other unidentified unemployment-related shocks ( $p^U_{ii}$ ), and this decomposition makes use of the orthogonalization of uncertainty shocks as described in the previous section. The second concerns the decomposition of the dynamic propagation of these uncertainty shocks ( $p^U_{ii}$ ) into the components due to national dynamics ( $p^{NU}_{ii}$ ) relative to state-specific dynamics ( $p^{SU}_{ii}$ ), focusing on the infinite horizon effect on state-specific unemployment.

Figure 6 reports the ratio: $\frac{p_{ii}^{NU}}{p_{ii}^{U}}$ in a heatmap of the USA, which gives the relative importance of national dynamics versus both state and national dynamics, as modeled in equation (3), in terms of respective measures of the persistent effect of the above-defined uncertainty shocks on state-specific unemployment. The persistence measures are scaled by a standard error state-specific unemployment shock on impact. A simple correlation between the statistics for each state represented in Figure 5 and those in Figure 6 gives a value of 0.4 showing that national influences play a clear role in propagating the effects of uncertainty. On average, the uncertainty shocks transmitted through the channels associated with national elements account for 37% of the total variation in state-specific unemployment and the remaining 63% is attributed to the purely state-specific channel abstracting entirely from national dynamics. However, the figure also shows that there is a significant degree of heterogeneity across the US states. The figure also shows that the more central states in the USA seem to be less affected by national dynamics in the influence of uncertainty on economic activity—such as in the states of Texas, New Mexico, or Colorado, for instance. On the other hand, unemployment in the eastern states tend to be far more influenced by national elements in the propagation of uncertainty shocks. Factors that might explain such heterogeneity could include state-specific characteristics such as the state-level industry composition, fiscal constraints, labor market constraints, and financial frictions. We explore these patterns in terms of potential pointers toward an economic narrative in more detail in the next section.

Figure 6. US heatmap—relative importance of national uncertainty. Notes: This figure plots $\frac{p^{NU}_{ii}}{p^U_{ii}}$ , which measures the relative importance of national influences in propagating uncertainty shocks on state $i$ ’s unemployment.

5.1 Heterogeneity of State-Level Responses of Unemployment

The regression strategy involves starting with an initial regression of $\rho _{i}=\text{response}_{i}$ and solely considering the first set of explanatory variables which includes variables representing state industry structures and relevant variables. Starting with just one industry variable, and retaining only if statistically significant (at the 10% level of significance), other industry variables are introduced sequentially in subsequent regressions, once again retaining significant variables in the regression. In the following regressions, additional control variables from the other sets of regressors are introduced one by one in sequential regressions and only retained if statistically significant. Table 5 reports the coefficients from these sequential regressions.

Table 5. Heterogeneity analysis on the response of state-level unemployment to an aggregate uncertainty shock

Notes: $\text{response}_i$ is defined in Section 4.3 and represents the peak state-level response of unemployment to an aggregate uncertainty shock. White-corrected standard errors are in parentheses $^{***}p\lt 0.01, ^{**}p\lt 0.05, ^{*}p\lt 0.1$ .

Table 6. Heterogeneity analysis on the importance of national influences in propagating uncertainty shocks

Notes: $\frac{p^{NU}_{ii}}{p^U_{ii}}$ is defined in Section 4.4 and represents the relative importance of national uncertainty shocks in propagating uncertainty shocks. White-corrected standard errors are in parentheses $^{***}p\lt 0.01$ , $^{**}p\lt 0.05$ , $^{*}p\lt 0.1$ .

Table 5 Column 1 presents our benchmark regression result from the first sequence of regressions relating the estimated responses $\rho _{i}$ to variables accounting for the structure of industry in each state where only the remaining significant industry variables are reported.Footnote ²² The column shows that only the share of the manufacturing and the mining industry have a robust and significant relationship with the responses of unemployment rate to an increase in US-wide uncertainty. These findings on the industry mix are completely consistent with those reported in Mumtaz et al. (Reference Mumtaz, Sunder-Plassmann and Theophilopoulou2018). We find that states with a higher concentration of the manufacturing industry experience a larger increase in unemployment after an increase in US-wide uncertainty. While speculative, this is consistent with the precautionary saving channel of uncertainty shocks causing a reduction in demand for manufacturing goods. On the other hand, we find that states with a larger mining industry experience a relatively smaller increase in unemployment. As documented in many studies such as Jo (Reference Jo2014), Mumtaz et al. (Reference Mumtaz, Sunder-Plassmann and Theophilopoulou2018) or Tran (Reference Tran2021), for instance, there is evidence that an uncertainty shock results in an increase in the price of some commodities. If this is the case, then the increase in commodity prices could be a contributing factor in negating the negative effects of uncertainty in states with a higher mining share of industry.

Column 2 and Column 3 of Table 5 show that the variables reflecting the housing market (Home Vacancy or Home Ownership) are not significant and are thus excluded from the subsequent regression specifications. Columns 4–10 present the results of sequentially including variables reflecting: labor market conditions (i.e. Right to Work or Union Membership); financial conditions; and the fiscal condition (state-level debt, state-level spending, and intergovernmental transfers). We find that none of these variables exhibit a statistically significant relationship with the responses of unemployment to state-level uncertainty—with Manufacturing and Mining still remaining significant in most of these regressions. There is good evidence, therefore, to support the results reported in Column 1. Findings from these subsequent regressions (Column 2 onward), however, are in contrast to the results in Mumtaz et al. (Reference Mumtaz, Sunder-Plassmann and Theophilopoulou2018) who report a significant association between the effect of uncertainty and the state-level housing market, the fiscal condition, and the financial constraint. The difference in findings could be due to differences in the sample period (Mumtaz et al. (Reference Mumtaz, Sunder-Plassmann and Theophilopoulou2018) cover the period 1960Q1–2014Q1) and also the fact that the authors study the response of quarterly real income growth to an uncertainty shock. When we use unemployment as a measure of real economic activity and in a framework accommodating state interactions and feedbacks, the relationship between these variables and uncertainty shocks is weaker.

In summary, the benchmark estimates and the detailed robustness checks suggest the following results. First, states with a higher concentration of the manufacturing industry experience a larger increase in unemployment when impacted by an uncertainty shock. Second, states with a higher concentration of the mining industry appear to be affected less by this shock.

5.2 Heterogeneity of National Influences in the Propagation of Uncertainty Shocks

In this section, we employ the same regression and testing strategy as described in the previous section, with the dependent variable now $\rho _{i}=\frac{p_{ii}^{NU}}{p_{ii}^{U}}.$ Again, starting with a set of sequential regressions involving the first set of variables reflecting the industry structure (and as detailed in the Appendix), we end up with an industry mix involving Government and Real Estate remaining as the significant variables as the initial baseline regression and as reported in Column 1 of Table 6. To this baseline regression, we add Home Vacancy in Column 2 and Home Ownership in Column 3. Given the statistical significance of Home Vacancy, we keep it in the regression specification and add in sequentially Right to Work in Column 4, Union membership in Column 5, and the degree of financial frictions in Column 6. None of these latter three variables prove to be statistically significant. Home Vacancy also drops out with the inclusion of the measure of state-level debt.Footnote ²³ We subsequently add in a measure of intergovernmental transfers as reported in Column 9. Although we find that the measure of intergovernmental transfers is statistically significant, we exclude this variable from the regression on the grounds that it takes on a value of almost 0, reduces the overall goodness-of-fit of the model as seen by the adjusted $R^{2}$ measure in Columns 8–10, and its inclusion takes away from the significance of the share of the government sector which has been a robust explanatory variable in all the other regressions.

Our preferred specification is as in Column 8. The results in this column shows that only the government sector, the real estate industry, and the state-level of fiscal conditions are robust in terms of statistical significance in terms of the association the relative importance of the national influences in propagating uncertainty shocks. We find that states with a higher concentration of the real estate industry reflect a tendency for a state to experience a larger impact through national influences in propagating uncertainty shocks. The finding of the relatively greater importance of the national factors is consistent an increased degree of contagion between the financial market and the real estate market during the GFC, reflecting the housing bubble and the subprime mortgage lending crisis [Caporin et al. (Reference Caporin, Gupta and Ravazzolo2021)].

On the other hand, states with a more active fiscal policy experience less of an influence from the national factors in the propagation of uncertainty shocks. We find a negative and statistically significant relationship between the importance of national influences in propagating uncertainty shocks and the share of the government sector and the size of the state-level debt. Our conjecture on the negative association between an active fiscal policy and the importance of national influences in propagating uncertainty shocks is further solidified when we replace state-level debt by state-level spending in Table 6 Column 11. We find that there is a significant association between state-level spending and the importance of national factors in the propagation of uncertainty shocks. Finally, the inclusion of the share of internet users in Column 12 does not affect the results of our preferred specification.

In summary, the results from our preferred regression specification and detailed robustness checks suggest the following: the relative importance of national factors in the propagation of uncertainty shocks tends to be (i) smaller in states with a more active fiscal policy and (ii) greater in states with a larger concentration of the real estate industry.